An optimization-based method for prediction of lumbar spine segmental kinematics from the measurements of thorax and pelvic kinematics

Towards improving the accuracy of musculoskeletal simulation of dynamic three-dimensional spine rotations with optimizing model and algorithm

BACKGROUND

The accuracy of musculoskeletal simulations greatly relies on model structures and optimization algorithms. This study investigated the unclarified influence of accounting for several commonly-simplified different model components and optimization criteria on spinal musculoskeletal simulations.

METHODS

The study constructed a full-body musculoskeletal model with passive components of functional spinal units and spinal muscles subject-specifically refined. A muscle redundancy solver was built with 15 optimization criteria. Three-dimensional spine rotations and spinal muscle activities were measured using optical motion capture and electromyogram techniques when eight healthy volunteers performed standing, flexion/extension, lateral bending, and axial rotation. The effect of the model with four different conditions of the passive components and the sensitivity of the 15 optimization criteria on simulations were investigated.

RESULTS

Accounting for the refined passive components significantly improved the simulation accuracy. Different optimization criteria behaved distinctly for different motions. Generally minimizing the sum of squared muscle activations outperformed the others, with the highest averaged correlation coefficient (0.82) between the estimated erector spinae muscle activations and measured electromyography and with the estimated joint compression forces comparable to in vivo reference data.

CONCLUSION

This study highlights the importance of passive model components and proposes a suitable optimization framework for realistic spinal musculoskeletal simulations.

The Influence of Kinematic Constraints on Model Performance During Inverse Kinematics Analysis of the Thoracolumbar Spine

Motion analysis is increasingly applied to spine musculoskeletal models using kinematic constraints to estimate individual intervertebral joint movements, which cannot be directly measured from the skin surface markers. Traditionally, kinematic constraints have allowed a single spinal degree of freedom (DOF) in each direction, and there has been little examination of how different kinematic constraints affect evaluations of spine motion. Thus, the objective of this study was to evaluate the performance of different kinematic constraints for inverse kinematics analysis. We collected motion analysis marker data in seven healthy participants (4F, 3M, aged 27–67) during flexion–extension, lateral bending, and axial rotation tasks. Inverse kinematics analyses were performed on subject-specific models with 17 thoracolumbar joints allowing 51 rotational DOF (51DOF) and corresponding models including seven sets of kinematic constraints that limited spine motion from 3 to 9DOF. Outcomes included: (1) root mean square (RMS) error of spine markers (measured vs. model); (2) lag-one autocorrelation coefficients to assess smoothness of angular motions; (3) maximum range of motion (ROM) of intervertebral joints in three directions of motion (FE, LB, AR) to assess whether they are physiologically reasonable; and (4) segmental spine angles in static ROM trials. We found that RMS error of spine markers was higher with constraints than without (p < 0.0001) but did not notably improve kinematic constraints above 6DOF. Compared to segmental angles calculated directly from spine markers, models with kinematic constraints had moderate to good intraclass correlation coefficients (ICCs) for flexion–extension and lateral bending, though weak to moderate ICCs for axial rotation. Adding more DOF to kinematic constraints did not improve performance in matching segmental angles. Kinematic constraints with 4–6DOF produced similar levels of smoothness across all tasks and generally improved smoothness compared to 9DOF or unconstrained (51DOF) models. Our results also revealed that the maximum joint ROMs predicted using 4–6DOF constraints were largely within physiologically acceptable ranges throughout the spine and in all directions of motions. We conclude that a kinematic constraint with 5DOF can produce smooth spine motions with physiologically reasonable joint ROMs and relatively low marker error.

Trunk-Pelvis motions and spinal loads during upslope and downslope walking among persons with transfemoral amputation

Larger trunk and pelvic motions in persons with (vs. without) lower limb amputation during activities of daily living (ADLs) adversely affect the mechanical demands on the lower back. Building on evidence that such altered motions result in larger spinal loads during level-ground walking, here we characterize trunk-pelvic motions, trunk muscle forces, and resultant spinal loads among sixteen males with unilateral, transfemoral amputation (TFA) walking at a self-selected speed both up ("upslope"; 1.06 ± 0.14 m/s) and down ("downslope"; 0.98 ± 0.20 m/s) a 10-degree ramp. Tri-planar trunk and pelvic motions were obtained (and ranges-of-motion [ROM] computed) as inputs for a non-linear finite element model of the spine to estimate global and local muscle (i.e., trunk movers and stabilizers, respectively) forces, and resultant spinal loads. Sagittal- (p = 0.001), frontal- (p = 0.004), and transverse-plane (p < 0.001) trunk ROM, and peak mediolateral shear (p = 0.011) and local muscle forces (p = 0.010) were larger (respectively 45, 35, 98, 70, and 11%) in upslope vs. downslope walking. Peak anteroposterior shear (p = 0.33), compression (p = 0.28), and global muscle (p = 0.35) forces were similar between inclinations. Compared to previous reports of persons with TFA walking on level ground, 5-60% larger anteroposterior and mediolateral shear observed here (despite ∼0.25 m/s slower walking speeds) suggest greater mechanical demands on the low back in sloped walking, particularly upslope. Continued characterization of trunk motions and spinal loads during ADLs support the notion that repeated exposures to these larger-than-normal (i.e., vs. level-ground walking in TFA and uninjured cohorts) spinal loads contribute to an increased risk for low back injury following lower limb amputation.

Trunk muscle forces and spinal loads in persons with unilateral transfemoral amputation during sit-to-stand and stand-to-sit activities

BACKGROUND

Alterations and asymmetries in trunk motions during activities of daily living, involving lower extremities, are suggested to cause higher spinal loads in persons with unilateral lower limb amputation. Given the repetitive nature of most activities of daily living, knowledge of the amount of increase in spinal loads is important for designing interventions aimed at prevention of secondary low back pain due to potential fatigue failure of spinal tissues. The objective of this study was to determine differences in trunk muscle forces and spinal loads between persons with and without lower limb amputation when performing sit-to-stand and stand-to-sit tasks.

METHODS

Kinematics of the pelvis and thorax, obtained from ten males with unilateral transfemoral lower limb amputation and 10 male uninjured controls when performing sit-to-stand and stand-to-sit activities, were used within a non-linear finite element model of the spine to estimate trunk muscle forces and resultant spinal loads.

FINDINGS

The peak compression force, medio-lateral (only during stand-to-sit), and antero-posterior shear forces were respectively 348 N, 269 N, and 217 N larger in person with vs. without amputation. Persons with amputation also experienced on average 171 N and 53 N larger mean compression force and medio-lateral shear force, respectively.

INTERPRETATION

While spinal loads were larger in persons with amputation, these loads were generally smaller than the reported threshold for spinal tissue injury. However, a rather small increase in spinal loads during common activities of daily living like walking, sit-to-stand, and stand-to-sit may nevertheless impose a significant risk of fatigue failure for spinal tissues due to the repetitive nature of these activities.

Human body modeling method to simulate the biodynamic characteristics of spine in vivo with different sitting postures

The aim of this study is to model the computational model of seated whole human body including skeleton, muscle, viscera, ligament, intervertebral disc, and skin to predict effect of the factors (sitting postures, muscle and skin, buttocks, viscera, arms, gravity, and boundary conditions) on the biodynamic characteristics of spine. Two finite element models of seated whole body and a large number of finite element models of different ligamentous motion segments were developed and validated. Static, modal, and transient dynamic analyses were performed. The predicted vertical resonant frequency of seated body model was in the range of vertical natural frequency of 4 to 7 Hz. Muscle, buttocks, viscera, and the boundary conditions of buttocks have influence on the vertical resonant frequency of spine. Muscle played a very important role in biodynamic response of spine. Compared with the vertical posture, the posture of lean forward or backward led to an increase in stress on anterior or lateral posterior of lumbar intervertebral discs. This indicated that keeping correct posture could reduce the injury of vibration on lumbar intervertebral disc under whole-body vibration. The driving posture not only reduced the load of spine but also increased the resonant frequency of spine.

A model-based approach for estimation of changes in lumbar segmental kinematics associated with alterations in trunk muscle forces

The kinematics information from imaging, if combined with optimization-based biomechanical models, may provide a unique platform for personalized assessment of trunk muscle forces (TMFs). Such a method, however, is feasible only if differences in lumbar spine kinematics due to differences in TMFs can be captured by the current imaging techniques. A finite element model of the spine within an optimization procedure was used to estimate segmental kinematics of lumbar spine associated with five different sets of TMFs. Each set of TMFs was associated with a hypothetical trunk neuromuscular strategy that optimized one aspect of lower back biomechanics. For each set of TMFs, the segmental kinematics of lumbar spine was estimated for a single static trunk flexed posture involving, respectively, 40° and 10° of thoracic and pelvic rotations. Minimum changes in the angular and translational deformations of a motion segment with alterations in TMFs ranged from 0° to 0.7° and 0 mm to 0.04 mm, respectively. Maximum changes in the angular and translational deformations of a motion segment with alterations in TMFs ranged from 2.4° to 7.6° and 0.11 mm to 0.39 mm, respectively. The differences in kinematics of lumbar segments between each combination of two sets of TMFs in 97% of cases for angular deformation and 55% of cases for translational deformation were within the reported accuracy of current imaging techniques. Therefore, it might be possible to use image-based kinematics of lumbar segments along with computational modeling for personalized assessment of TMFs.

Viscoelastic Response of the Human Lower Back to Passive Flexion: The Effects of Age

Low back pain is a leading cause of disability in the elderly. The potential role of spinal instability in increasing risk of low back pain with aging was indirectly investigated via assessment of age-related differences in viscoelastic response of lower back to passive deformation. The passive deformation tests were conducted in upright standing posture to account for the effects of gravity load and corresponding internal tissues responses on the lower back viscoelastic response. Average bending stiffness, viscoelastic relaxation, and dissipated energy were quantified to characterize viscoelastic response of the lower back. Larger average bending stiffness, viscoelastic relaxation and dissipated energy were observed among older vs. younger participants. Furthermore, average bending stiffness of the lower back was found to be the highest around the neutral standing posture and to decrease with increasing the lower back flexion angle. Larger bending stiffness of the lower back at flexion angles where passive contribution of lower back tissues to its bending stiffness was minimal (i.e., around neutral standing posture) highlighted the important role of active vs. passive contribution of tissues to lower back bending stiffness and spinal stability. As a whole our results suggested that a diminishing contribution of passive and volitional active subsystems to spinal stability may not be a reason for higher severity of low back pain in older population. The role of other contributing elements to spinal stability (e.g., active reflexive) as well as equilibrium-based parameters (e.g., compression and shear forces under various activities) in increasing severity of low back pain with aging should be investigated in future.

Persons with unilateral transfemoral amputation experience larger spinal loads during level-ground walking compared to able-bodied individuals

BACKGROUND

Persons with lower limb amputation walk with increased and asymmetric trunk motion; a characteristic that is likely to impose distinct demands on trunk muscles to maintain equilibrium and stability of the spine. However, trunk muscle responses to such changes in net mechanical demands, and the resultant effects on spinal loads, have yet to be determined in this population.

METHODS

Building on a prior study, trunk and pelvic kinematics collected during level-ground walking from 40 males (20 with unilateral transfemoral amputation and 20 matched controls) were used as inputs to a kinematics-driven, nonlinear finite element model of the lower back to estimate forces in 10 global (attached to thorax) and 46 local (attached to lumbar vertebrae) trunk muscles, as well as compression, lateral, and antero-posterior shear forces at all spinal levels.

FINDINGS

Trunk muscle force and spinal load maxima corresponded with heel strike and toe off events, and among persons with amputation, were respectively 10-40% and 17-95% larger during intact vs. prosthetic stance, as well as 6-80% and 26-60% larger during intact stance relative to controls.

INTERPRETATION

During gait, larger spinal loads with transfemoral amputation appear to be the result of a complex pattern of trunk muscle recruitment, particularly involving co-activation of antagonistic muscles during intact limb stance; a period when these individuals are confident and likely to use the trunk to assist with forward progression. Given the repetitive nature of walking, repeated exposure to such elevated loading likely increases the risk for low back pain in this population.

Age-related differences in trunk intrinsic stiffness

Age-related differences in trunk intrinsic stiffness, as an important potential contributor to spinal stability, were investigated here because of: (1) the role of spinal instability in low back pain (LBP) development; (2) the increasing prevalence of LBP with age, and (3) the increasing population of older people in the workforce. Sixty individuals aged 20-70 years, in five equal-size age groups, completed a series of displacement-controlled perturbation tests in an upright standing posture while holding four different levels of trunk extension efforts. In addition to examining any age-related difference in trunk intrinsic stiffness, the current design assessed the effects of gender, level of effort, and any differences in lower back neuromuscular patterns on trunk intrinsic stiffness. No significant differences in trunk intrinsic stiffness were found between the age groups. However, stiffness was significantly larger among males and increased with the level of extension effort. No influences of differences in neuromuscular pattern were observed. Since the passive contribution of trunk tissues in the upright standing posture is minimal, our values of estimated trunk intrinsic stiffness primarily represent the volitional contribution of the lower back musculoskeletal system to spinal stability. Therefore, it seems unlikely that the alterations in volitional behavior of the lower back musculature, caused by aging (e.g., as reflected in reduced strength), diminish their contributions to the spinal stability.